I just changed my store to the Minimal theme and have two critical issues. The first (most important) is that there is no visible "view cart" icon anywhere on desktop or mobile. This means that a customer who has added to a cart but is still browsing can not go back to their cart to complete a purchase without adding another product. I need to have a "view cart" icon/button on the header, preferably top right (my search bar is in the header, top left). Second issue: there is no search bar on the mobile version.
As I know these feature are inbuilt in Minimal theme and when I check in theme demo here https://minimal-fashion.myshopify.com/ I find yes these features are available in it.
May be you are missing something or may be I can't understand your post properly.